Write an equation for the parabola.
-vertex $( 6 , - 7 )$, focus $( 9 , - 7 )$
A) $( x - 6 ) ^ { 2 } = 12 ( y + 7 )$
B) $\frac { 3 } { 4 } ( x - 6 ) = ( y + 7 ) ^ { 2 }$
C) $x - 6 = 3 ( y + 7 ) ^ { 2 }$
D) $( y + 7 ) ^ { 2 } = 12 ( x - 6 )$

Question

Quizplus · Accepted Answer

The parabola opens horizontally since the focus and vertex have the same y-coordinate but different x-coordinates. The distance between the vertex and focus, $p = 3$, is positive, indicating the parabola opens to the right. The standard form for a horizontal parabola is $(y - k)^2 = 4p(x - h)$, where $(h, k)$ is the vertex. Substituting $h = 6$, $k = -7$, and $p = 3$ gives $(y + 7)^2 = 12(x - 6)$.

Write an Equation for the Parabola (6,−7)( 6 , - 7 )(6,−7)

Write an Equation for the Parabola $( 6 , - 7 )$